Download Neural Networks

Artificial Neural Networks
Outline
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What are Neural Networks?
Biological Neural Networks
ANN – The basics
Feed forward net
Training
Example – Voice recognition
Applications – Feed forward nets
Recurrency
Elman nets
Hopfield nets
Central Pattern Generators
Conclusion
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What are Neural Networks?
• Models of the brain and nervous system
• Highly parallel
– Process information much more like the brain than a serial
computer
• Learning
• Very simple principles
• Very complex behaviors
• Applications
– As powerful problem solvers
– As biological models
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Biological Neural Nets
• Pigeons as art experts (Watanabe et al. 1995)
– Experiment:
• Pigeon in Skinner box
• Present paintings of two different artists (e.g. Chagall / Van
Gogh)
• Reward for pecking when presented a particular artist (e.g. Van
Gogh)
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• Pigeons were able to discriminate between Van Gogh
and Chagall with 95% accuracy (when presented with
pictures they had been trained on)
• Discrimination still 85% successful for previously
unseen paintings of the artists
• Pigeons do not simply memorise the pictures
• They can extract and recognise patterns (the ‘style’)
• They generalise from the already seen to make
predictions
• This is what neural networks (biological and artificial)
are good at (unlike conventional computer)
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ANNs (Artificial Neural Network)
The basics
• ANNs incorporate the two fundamental components
of biological neural nets:
1. Neurones (nodes)
2. Synapses (weights)
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• Neurone vs. Node
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• Structure of a node:
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Squashing function limits node output:
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• Synapse vs. weight
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Feed-forward nets
• Information flow is unidirectional
• Data is presented to Input layer
• Passed on to Hidden Layer
• Passed on to Output layer
• Information is distributed
• Information processing is parallel
Internal representation (interpretation) of data
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• Feeding data through the net:
(1  0.25) + (0.5  (-1.5)) = 0.25 + (-0.75) = - 0.5
Squashing:
1
0.3775
0
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1e
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• Data is presented to the network in the form of
activations in the input layer
• Examples
– Pixel intensity (for pictures)
– Molecule concentrations (for artificial nose)
– Share prices (for stock market prediction)
• Data usually requires preprocessing
– Analogous to senses in biology
• How to represent more abstract data, e.g. a name?
– Choose a pattern, e.g.
• 0-0-1 for “Chris”
• 0-1-0 for “Becky”
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• Weight settings determine the behavior of a network
 How can we find the right weights?
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Training the Network - Learning
• Backpropagation
– Requires training set (input / output pairs)
– Starts with small random weights
– Error is used to adjust weights (supervised learning)
 Gradient descent on error landscape
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• Advantages
– It works!
– Relatively fast
• Downsides
– Requires a training set
– Can be slow
– Probably not biologically realistic
• Alternatives to Backpropagation
– Hebbian learning
• Not successful in feed-forward nets
– Reinforcement learning
• Only limited success
– Artificial evolution
• More general, but can be even slower than backprop
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Example: Voice Recognition
• Task: Learn to discriminate between two different
voices saying “Hello”
• Data
– Sources
• Steve Simpson
• David Raubenheimer
– Format
• Frequency distribution (60 bins)
• Analogy: cochlea
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• Network architecture
– Feed forward network
• 60 input (one for each frequency bin)
• 6 hidden
• 2 output (0-1 for “Steve”, 1-0 for “David”)
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• Presenting the data
Steve
David
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• Presenting the data (untrained network)
Steve
0.43
0.26
David
0.73
0.55
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• Calculate error
Steve
0.43 – 0
= 0.43
0.26 –1
= 0.74
0.73 – 1
= 0.27
0.55 – 0
= 0.55
David
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• Backprop error and adjust weights
Steve
0.43 – 0
= 0.43
0.26 – 1
= 0.74
1.17
David
0.73 – 1
= 0.27
0.55 – 0
= 0.55
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0.82
• Repeat process (sweep) for all training pairs
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Present data
Calculate error
Backpropagate error
Adjust weights
• Repeat process multiple times
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• Presenting the data (trained network)
Steve
0.01
0.99
David
0.99
0.01
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• Results – Voice Recognition
– Performance of trained network
• Discrimination accuracy between known “Hello”s
– 100%
• Discrimination accuracy between new “Hello”’s
– 100%
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• Results – Voice Recognition
– Network has learned to generalize from original data
– Networks with different weight settings can have same
functionality
– Trained networks ‘concentrate’ on lower frequencies
– Network is robust against non-functioning nodes
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Applications of Feed-forward nets
– Pattern recognition
• Character recognition
• Face Recognition
– Sonar mine/rock recognition (Gorman & Sejnowksi, 1988)
– Navigation of a car (Pomerleau, 1989)
– Stock-market prediction
– Pronunciation (NETtalk)
(Sejnowksi & Rosenberg, 1987)
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Cluster analysis of hidden layer
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FFNs as Biological Modelling Tools
• Signalling
– Enquist & Arak (1994)
• Preference for symmetry not selection for ‘good genes’, but
instead arises through the need to recognise objects
irrespective of their orientation
– Johnstone (1994)
• Exaggerated, symmetric ornaments facilitate mate recognition
(but see Dawkins & Guilford, 1995)
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Recurrent Networks
• Feed forward networks:
– Information only flows one way
– One input pattern produces one output
– No sense of time (or memory of previous state)
• Recurrency
– Nodes connect back to other nodes or themselves
– Information flow is multidirectional
– Sense of time and memory of previous state(s)
• Biological nervous systems show high levels of
recurrency (but feed-forward structures exists too)
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Elman Nets
• Elman nets are feed forward networks with partial
recurrency
• Unlike feed forward nets, Elman nets have a memory
or sense of time
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Classic experiment on language acquisition and
processing (Elman, 1990)
• Task
– Elman net to predict successive words in sentences.
• Data
– Suite of sentences, e.g.
• “The boy catches the ball.”
• “The girl eats an apple.”
– Words are input one at a time
• Representation
– Binary representation for each word, e.g.
• 0-1-0-0-0 for “girl”
• Training method
– Backpropagation
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• Internal representation of words
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Hopfield Networks
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Sub-type of recurrent neural nets
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Fully recurrent
Weights are symmetric
Nodes can only be on or off
Random updating
Learning: Hebb rule (cells that fire together wire
together)
– Biological equivalent to LTP and LTD
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Can recall a memory, if presented with a
corrupt or incomplete version
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auto-associative or
content-addressable memory
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Task:store images with resolution of 20x20 pixels
 Hopfield net with 400 nodes
Memorise:
1.
2.
Present image
Apply Hebb rule (cells that fire together, wire together)
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3.
Increase weight between two nodes if both have same activity, otherwise decrease
Go to 1
Recall:
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2.
3.
Present incomplete pattern
Pick random node, update
Go to 2 until settled
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• Memories are attractors in state space
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Catastrophic forgetting
• Problem: memorising new patterns corrupts the memory of older
ones
 Old memories cannot be recalled, or spurious memories arise
• Solution: allow Hopfield net to sleep
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• Two approaches (both using randomness):
– Unlearning (Hopfield, 1986)
• Recall old memories by random stimulation, but use an inverse
Hebb rule
‘Makes room’ for new memories (basins of attraction shrink)
– Pseudorehearsal (Robins, 1995)
• While learning new memories, recall old memories by random
stimulation
• Use standard Hebb rule on new and old memories
 Restructure memory
• Needs short-term + long term memory
• Mammals: hippocampus plays back new memories to neocortex, which is randomly stimulated at the same time
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RNNs as Central Pattern Generators
• CPGs: group of neurones creating rhythmic muscle activity for
locomotion, heart-beat etc.
• Identified in several invertebrates and vertebrates
• Hard to study
  Computer modelling
– E.g. lamprey swimming (Ijspeert et al., 1998)
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• Evolution of Bipedal Walking (Reil & Husbands, 2001)
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0.9
0.8
activation
0.7
left hip lateral
left hip a/p
0.6
right hip lateral
0.5
right hip a/p
0.4
left knee
right knee
0.3
0.2
0.1
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9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77
time
• CPG cycles are cyclic attractors in state space
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Summary – Neural Networks
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Components – biological plausibility
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Feed forward networks
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Neurone / node
Synapse / weight
Unidirectional flow of information
Good at extracting patterns, generalisation and
prediction
Distributed representation of data
Parallel processing of data
Training: Backpropagation
Not exact models, but good at demonstrating
principles
Recurrent networks
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Multidirectional flow of information
Memory / sense of time
Complex temporal dynamics (e.g. CPGs)
Various training methods (Hebbian, evolution)
Often better biological models than FFNs
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